Intermolecular forces and properties of fluid. I. The automatic calculation of higher virial coefficients and some values of the fourth coefficient for the Lennard-Jones potential

1960 ◽  
Vol 254 (1279) ◽  
pp. 487-498 ◽  
Keyword(s):  
Virial Coefficient ◽  
Mathematical Problem ◽  
Virial Coefficients ◽  
Intermolecular Forces ◽  
Lennard Jones Potential ◽  
Intermolecular Potentials ◽  
Jones Potential ◽  
Lennard Jones ◽  
Experimental Values ◽  
First Time

The prediction of the virial coefficients for particular intermolecular potentials is generally regarded as a difficult mathematical problem. Methods have only been available for the second and third coefficient and in fact only few calculations have been made for the latter. Here a new method of successive approximation is introduced which has enabled the fourth virial coefficient to be evaluated for the first time for the Lennard-Jones potential. It is particularly suitable for automatic computation and the values reported here have been obtained by the use of the EDSAC I. The method is applicable to other potentials and some values for these will be reported subsequently. The values obtained cannot yet be compared with any experimental results since these have not been measured, but they can be used in the meantime to obtain more accurate experimental values of the lower coefficients.

COMPRESSIBILITY OF GASES AT HIGH TEMPERATURES: IX. SECOND VIRIAL COEFFICIENTS AND THE INTERMOLECULAR POTENTIAL OF NEON

1955 ◽  
Vol 33 (4) ◽  
pp. 589-596 ◽  
Author(s):  
G. A. Nicholson ◽  
W. G. Schneider
Keyword(s):  
Low Temperature ◽  
High Temperatures ◽  
Pressure Range ◽  
Virial Coefficients ◽  
Intermolecular Potential ◽  
Lennard Jones Potential ◽  
Intermolecular Potentials ◽  
Jones Potential ◽  
Second Virial Coefficients ◽  
Lennard Jones

The second virial coefficients of neon have been determined in the temperature range 0° to 700 °C. and the pressure range 10 to 80 atmospheres. These data were combined with published low temperature (−150° to 0 °C.) second virial data, to investigate the intermolecular potentials of neon using both a Lennard-Jones potential, with a 9th and 12th power repulsion term, and also a modified Buckingham exponential–six potential. The agreement between observed and calculated values of B(T) was excellent for both the exponential–six and the Lennard-Jones 12:6 potentials and slightly less satisfactory for the Lennard-Jones 9:6 potential.

Second virial coefficient of a generalized Lennard-Jones potential

2015 ◽  
Vol 142 (3) ◽  
pp. 034305 ◽  
Author(s):  
Alfredo González-Calderón ◽  
Adrián Rocha-Ichante
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones

The behaviour of fluids of Quasi-Spherical molecules. I. Gases at low densities

1954 ◽  
Vol 7 (1) ◽  
pp. 1 ◽  
Author(s):  
SD Hamann ◽  
JA Lambert
Keyword(s):  
Potential Energy ◽  
Interaction Energy ◽  
Good Description ◽  
Virial Coefficients ◽  
Polyatomic Molecules ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones

Consideration of the spherically smoothed mutual potential energy between nearly spherical polyatomic molecules leads to the conclusion that it can often be well represented by a (28,7) type of Lennard-Jones potential. Second and third virial coefficients have been calculated for this potential and also for (∞,6) and (∞,7) potentials. The (28,7) interaction energy gives a good description of the properties of gases of quasi-spherical molecules. For these gases it is markedly superior to the more usual (12,6) potential.

Intermolecular forces and properties of fluids II. A general functional representation of inter molecular potentials, and some values of the second, third and fourth virial coefficients for systematically differing potentials

1960 ◽  
Vol 254 (1279) ◽  
pp. 499-506 ◽  
Keyword(s):  
Experimental Data ◽  
Complete System ◽  
Virial Coefficients ◽  
Intermolecular Forces ◽  
Potential Well ◽  
Intermolecular Potentials ◽  
Lennard Jones ◽  
Functional Representation ◽  
Single Term ◽  
Molecular Potentials

A new functional representation of angle-independent intermolecular potentials is described, having an unlimited number of parameters in the form of linear coefficients in an expansion depending on a complete system of functions. The basic single-term form of th is function is practically equivalent to the Lennard-Jones (6-12) potential. Three particular examples of this potential, having different widths of the potential well, have been examined, and the second, third, and fourth virial coefficients for them have been calculated for a number of temperatures. It is shown that the new functional representation should enable better and more systematic progress in the estimation of intermolecular potentials to fit experimental data.

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